Battista (mathematics education, Ohio State U.) outlines cognition-based assessment (CBA), an approach for teaching elementary math (specifically multiplication and division in this volume) that can be used with any curriculum and enables all students at the elementary level to understand, make sense of, and become proficient in the subject. It emphasizes deep understanding and reasoning within the context of continual assessment and understanding students' mathematical thinking, then building on that thinking with instruction (rather than teaching fixed content) and focusing on optimizing individual progress. He provides research-based descriptions of students' development of understanding core ideas and reasoning processes in math, including their cognitive barriers and fundamental mental processes; assessment tasks that ascertain how students are reasoning at different levels of sophistication; and suggestions for differentiated instructional activities to help students move to higher levels. The volume is one of six on the approach and can be integrated with the tiers of response to intervention. Student work samples and assessment tasks are provided. There is no index. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)